Results for 'Invariant equivalence relations'

1000+ found
Order:
  1.  35
    Simultaneity as an Invariant Equivalence Relation.Marco Mamone-Capria - 2012 - Foundations of Physics 42 (11):1365-1383.
    This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in ℝ4 is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament’s theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2.  25
    Smoothness of Bounded Invariant Equivalence Relations.Krzysztof Krupiński & Tomasz Rzepecki - 2016 - Journal of Symbolic Logic 81 (1):326-356.
  3.  9
    Equivalence Relations Invariant Under Group Actions.Tomasz Rzepecki - 2018 - Journal of Symbolic Logic 83 (2):683-702.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  4.  10
    Relative Exchangeability with Equivalence Relations.Harry Crane & Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):533-556.
    We describe an Aldous–Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the results on relative exchangeability due to Ackerman \)-invariant measures: part I, 2015. arXiv:1509.06170) and Crane and Towsner and hierarchical exchangeability results due to Austin and Panchenko :809–823, 2014).
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  22
    On Σ11 Equivalence Relations Over the Natural Numbers.Ekaterina B. Fokina & Sy‐David Friedman - 2012 - Mathematical Logic Quarterly 58 (1-2):113-124.
    We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  6.  9
    On Bounded Type-Definable Equivalence Relations.Ludomir Newelski & Krzysztof Krupi?Ski - 2002 - Notre Dame Journal of Formal Logic 43 (4):231-242.
    We investigate some topological properties of the spaces of classes of bounded type-definable equivalence relations.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7.  41
    On Borel Equivalence Relations in Generalized Baire Space.Sy-David Friedman & Tapani Hyttinen - 2012 - Archive for Mathematical Logic 51 (3-4):299-304.
    We construct two Borel equivalence relations on the generalized Baire space κ κ , κ <κ = κ > ω, with the property that neither of them is Borel reducible to the other. A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy fails.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  7
    Abstraction Principles and the Classification of Second-Order Equivalence Relations.Sean C. Ebels-Duggan - 2019 - Notre Dame Journal of Formal Logic 60 (1):77-117.
    This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation E is defined without nonlogical vocabulary, then the bicardinal slice of any equivalence class—those equinumerous elements of the equivalence class with equinumerous complements—can have one of only three profiles. The improvements to Fine’s theorem (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  2
    Reducibility of Equivalence Relations Arising From Nonstationary Ideals Under Large Cardinal Assumptions.David Asperó, Tapani Hyttinen, Vadim Kulikov & Miguel Moreno - 2019 - Notre Dame Journal of Formal Logic 60 (4):665-682.
    Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10.  2
    On the Degree Structure of Equivalence Relations Under Computable Reducibility.Keng Meng Ng & Hongyuan Yu - 2019 - Notre Dame Journal of Formal Logic 60 (4):733-761.
    We study the degree structure of the ω-c.e., n-c.e., and Π10 equivalence relations under the computable many-one reducibility. In particular, we investigate for each of these classes of degrees the most basic questions about the structure of the partial order. We prove the existence of the greatest element for the ω-c.e. and n-computably enumerable equivalence relations. We provide computable enumerations of the degrees of ω-c.e., n-c.e., and Π10 equivalence relations. We prove that for all (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. Thin Equivalence Relations and Effective Decompositions.Greg Hjorth - 1993 - Journal of Symbolic Logic 58 (4):1153-1164.
    Let E be a Σ1 1 equivalence relation for which there does not exist a perfect set of inequivalent reals. If 0# exists or if V is a forcing extension of L, then there is a good ▵1 2 well-ordering of the equivalence classes.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  12.  13
    Borel Equivalence Relations Which Are Highly Unfree.Greg Hjorth - 2008 - Journal of Symbolic Logic 73 (4):1271-1277.
    There is an ergodic, measure preserving, countable Borel equivalence relation E on a standard Borel probability space (X, µ) such that E\c is not essentially free on any conull C ⊂ X.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  13.  16
    The {L}Aczkovich—{K}Omjáth Property for Coanalytic Equivalence Relations.Su Gao, Steve Jackson & Vincent Kieftenbeld - 2010 - Journal of Symbolic Logic 75 (3):1091-1101.
    Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark  
  14.  10
    Thin Equivalence Relations in Scaled Pointclasses.Ralf Schindler & Philipp Schlicht - 2011 - Mathematical Logic Quarterly 57 (6):615-620.
    For ordinals α beginning a Σ1 gap in equation image, where equation image is closed under number quantification, we give an inner model-theoretic proof that every thin equation image equivalence relation is equation image in a real parameter from the hypothesis equation image.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  15.  8
    Time-Intensity Equivalence Relations for Auditory Pulse Trains.Irwin Pollack - 1973 - Journal of Experimental Psychology 100 (2):239.
  16.  6
    Analytic Equivalence Relations and Bi-Embeddability.Sy-David Friedman & Luca Motto Ros - 2011 - Journal of Symbolic Logic 76 (1):243 - 266.
    Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L ω ₁ ω ) is far from complete (see (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  17.  18
    Recursively Enumerable Equivalence Relations Modulo Finite Differences.André Nies - 1994 - Mathematical Logic Quarterly 40 (4):490-518.
    We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th has the same computational complexity as the true first-order arithmetic.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  18.  44
    Countable Borel Equivalence Relations.S. Jackson, A. S. Kechris & A. Louveau - 2002 - Journal of Mathematical Logic 2 (01):1-80.
    This paper develops the foundations of the descriptive set theory of countable Borel equivalence relations on Polish spaces with particular emphasis on the study of hyperfinite, amenable, treeable and universal equivalence relations.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  19.  34
    The Effective Theory of Borel Equivalence Relations.Ekaterina B. Fokina, Sy-David Friedman & Asger Törnquist - 2010 - Annals of Pure and Applied Logic 161 (7):837-850.
    The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver [20] and Harrington, Kechris and Louveau [6] show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on , the power set of ω, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on . In this article (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  20.  5
    Borel Equivalence Relations and Classifications of Countable Models.Greg Hjorth & Alexander S. Kechris - 1996 - Annals of Pure and Applied Logic 82 (3):221-272.
    Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  21.  65
    Computably Enumerable Equivalence Relations.Su Gao & Peter Gerdes - 2001 - Studia Logica 67 (1):27-59.
    We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  22.  15
    Superrigidity and Countable Borel Equivalence Relations.Simon Thomas - 2003 - Annals of Pure and Applied Logic 120 (1-3):237-262.
    We formulate a Borel version of a corollary of Furman's superrigidity theorem for orbit equivalence and present a number of applications to the theory of countable Borel equivalence relations. In particular, we prove that the orbit equivalence relations arising from the natural actions of on the projective planes over the various p-adic fields are pairwise incomparable with respect to Borel reducibility.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  23. Classifying Positive Equivalence Relations.Claudio Bernardi & Andrea Sorbi - 1983 - Journal of Symbolic Logic 48 (3):529-538.
    Given two (positive) equivalence relations ∼ 1 , ∼ 2 on the set ω of natural numbers, we say that ∼ 1 is m-reducible to ∼ 2 if there exists a total recursive function h such that for every x, y ∈ ω, we have $x \sim_1 y \operatorname{iff} hx \sim_2 hy$ . We prove that the equivalence relation induced in ω by a positive precomplete numeration is complete with respect to this reducibility (and, moreover, a "uniformity (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  24.  7
    Analytic Equivalence Relations and Bi-Embeddability.Sy-David Friedman & Luca Motto Ros - 2011 - Journal of Symbolic Logic 76 (1):243-266.
    Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs is far from complete.In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  25.  8
    Borel Equivalence Relations Induced by Actions of the Symmetric Group.Greg Hjorth, Alexander S. Kechris & Alain Louveau - 1998 - Annals of Pure and Applied Logic 92 (1):63-112.
    We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  26. Maximal R.E. Equivalence Relations.Jeffrey S. Carroll - 1990 - Journal of Symbolic Logic 55 (3):1048-1058.
    The lattice of r.e. equivalence relations has not been carefully examined even though r.e. equivalence relations have proved useful in logic. A maximal r.e. equivalence relation has the expected lattice theoretic definition. It is proved that, in every pair of r.e. nonrecursive Turing degrees, there exist maximal r.e. equivalence relations which intersect trivially. This is, so far, unique among r.e. submodel lattices.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  27.  32
    Graphs Realised by R.E. Equivalence Relations.Alexander Gavruskin, Sanjay Jain, Bakhadyr Khoussainov & Frank Stephan - 2014 - Annals of Pure and Applied Logic 165 (7-8):1263-1290.
    We investigate dependence of recursively enumerable graphs on the equality relation given by a specific r.e. equivalence relation on ω. In particular we compare r.e. equivalence relations in terms of graphs they permit to represent. This defines partially ordered sets that depend on classes of graphs under consideration. We investigate some algebraic properties of these partially ordered sets. For instance, we show that some of these partial ordered sets possess atoms, minimal and maximal elements. We also fully (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  28.  9
    Popa Superrigidity and Countable Borel Equivalence Relations.Simon Thomas - 2009 - Annals of Pure and Applied Logic 158 (3):175-189.
    We present some applications of Popa’s Superrigidity Theorem to the theory of countable Borel equivalence relations. In particular, we show that the universal countable Borel equivalence relation E∞ is not essentially free.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  29.  3
    Classifying equivalence relations in the Ershov hierarchy.Nikolay Bazhenov, Manat Mustafa, Luca San Mauro, Andrea Sorbi & Mars Yamaleev - forthcoming - Archive for Mathematical Logic:1-30.
    Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ (...)
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  30. On Σ1 1 Equivalence Relations with Borel Classes of Bounded Rank.Ramez L. Sami - 1984 - Journal of Symbolic Logic 49 (4):1273 - 1283.
    In Baire space N = ω ω we define a sequence of equivalence relations $\langle E_\nu| \nu , each E v being Σ 1 1 with classes in Π 0 1 + ν + 1 and such that (i) E ν does not have perfectly many classes, and (ii) N/E ν is countable iff $\omega^L_\nu . This construction can be extended cofinally in (δ 1 3 ) L . A new proof is given of a theorem of Hausdorff (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  31.  23
    Cofinal Families of Borel Equivalence Relations and Quasiorders.Christian Rosendal - 2005 - Journal of Symbolic Logic 70 (4):1325-1340.
    Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B, are constructed. There is an analytic ideal on ω generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spaces, are shown to be Kσ complete.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  32.  33
    The Complexity of Hybrid Logics Over Equivalence Relations.Martin Mundhenk & Thomas Schneider - 2009 - Journal of Logic, Language and Information 18 (4):493-514.
    This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. For model checking, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PS pace , NE xp T ime , (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  33.  13
    Analytic Equivalence Relations and the Forcing Method.Jindřich Zapletal - 2013 - Bulletin of Symbolic Logic 19 (4):473-490.
    I describe several ways in which forcing arguments can be used to yield clean and conceptual proofs of nonreducibility, ergodicity and other results in the theory of analytic equivalence relations. In particular, I present simple Borel equivalence relations $E, F$ such that a natural proof of nonreducibility of $E$ to $F$ uses the independence of the Singular Cardinal Hypothesis at $\aleph_\omega$.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  34.  10
    Constructive Equivalence Relations on Computable Probability Measures.Laurent Bienvenu & Wolfgang Merkle - 2009 - Annals of Pure and Applied Logic 160 (3):238-254.
    A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computable probability measures where two measures are equivalent if they have the same set of random sequences. In what (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  35.  19
    An Algebraic Result About Soft Model Theoretical Equivalence Relations with an Application to H. Friedman's Fourth Problem.Daniele Mundici - 1981 - Journal of Symbolic Logic 46 (3):523-530.
    We prove the following algebraic characterization of elementary equivalence: $\equiv$ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if L = L ωω (Q i ) i ∈ ω (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  36.  14
    Complexity of Equivalence Relations and Preorders From Computability Theory.Egor Ianovski, Russell Miller, Keng Meng Ng & André Nies - 2014 - Journal of Symbolic Logic 79 (3):859-881.
    We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relationsR,S, a componentwise reducibility is defined byR≤S⇔ ∃f∀x, y[x R y↔fS f].Here,fis taken from a suitable class of effective functions. For us the relations will be on natural numbers, andfmust be computable. We show that there is a${\rm{\Pi }}_1^0$-complete equivalence relation, but no${\rm{\Pi }}_k^0$-complete fork≥ 2. We show that${\rm{\Sigma }}_k^0$preorders arising naturally in the above-mentioned areas are${\rm{\Sigma }}_k^0$-complete. This (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  37.  38
    ? 0 N -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351-358.
    In this paper we study the reducibility order m (defined in a natural way) over n 0 -equivalence relations. In particular, for every n> 0 we exhibit n 0 -equivalence relations which are complete with respect to m and investigate some consequences of this fact (see Introduction).
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  38.  24
    Treeable Equivalence Relations.Greg Hjorth - 2012 - Journal of Mathematical Logic 12 (1):1250003-.
    There are continuum many ≤B-incomparable equivalence relations induced by a free, Borel action of a countable non-abelian free group — and hence, there are 2α0 many treeable countable Borel equivalence relations which are incomparable in the ordering of Borel reducibility.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  39.  21
    Incomparable Treeable Equivalence Relations.Benjamin Miller - 2012 - Journal of Mathematical Logic 12 (1):1250004-.
    We establish Hjorth's theorem that there is a family of continuum-many pairwise strongly incomparable free actions of free groups, and therefore a family of continuum-many pairwise incomparable treeable equivalence relations.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  40.  5
    Cardinal Characteristics and Countable Borel Equivalence Relations.Samuel Coskey & Scott Schneider - 2017 - Mathematical Logic Quarterly 63 (3-4):211-227.
    Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number math formula. We analyze some of the basic behavior of these (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  41.  11
    Second-Order Logic on Equivalence Relations.Georgi Georgiev & Tinko Tinchev - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):229-246.
    In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  42.  12
    Property Τ and Countable Borel Equivalence Relations.Simon Thomas - 2007 - Journal of Mathematical Logic 7 (1):1-34.
    We prove Borel superrigidity results for suitably chosen actions of groups of the form SL2, where {p1, …, pt} is a finite nonempty set of primes, and present a number of applications to the theory of countable Borel equivalence relations. In particular, for each prime q, we prove that the orbit equivalence relations arising from the natural actions of SL2 on the projective lines ℚp ∪ {∞}, p ≠ q, over the various p-adic fields are pairwise (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  43. Canonization of Smooth Equivalence Relations on Infinite-Dimensional $Mathsf{E}_{0}$-Large Products.Vladimir Kanovei & Vassily Lyubetsky - 2020 - Notre Dame Journal of Formal Logic 61 (1):117-128.
    We propose a canonization scheme for smooth equivalence relations on Rω modulo restriction to E0-large infinite products. It shows that, given a pair of Borel smooth equivalence relations E, F on Rω, there is an infinite E0-large perfect product P⊆Rω such that either F⊆E on P, or, for some ℓ<ω, the following is true for all x,y∈P: xEy implies x=y, and x↾=y↾ implies xFy.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  44.  19
    Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF.Thomas Forster - 2016 - Philosophia Mathematica 24 (1):nku005.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for “low” sets, and thus, for example, a set of all ordinals. However, that set has an ordinal in turn which is not a member of the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  45.  9
    Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF.Thomas Forster - 2016 - Philosophia Mathematica 24 (1):50-59.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted _aussonderung_ but there are set theories which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for "low" sets, and thus, for example, a set of all ordinals. However, that set has an ordinal in turn which is not a member of the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  46.  40
    Algebraic Biology: Creating Invariant Binding Relations for Biochemical and Biological Categories. [REVIEW]Jerry L. R. Chandler - 2009 - Axiomathes 19 (3):297-320.
    The desire to understand the mathematics of living systems is increasing. The widely held presupposition that the mathematics developed for modeling of physical systems as continuous functions can be extended to the discrete chemical reactions of genetic systems is viewed with skepticism. The skepticism is grounded in the issue of scientific invariance and the role of the International System of Units in representing the realities of the apodictic sciences. Various formal logics contribute to the theories of biochemistry and molecular biology (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  47.  26
    Precursors to Number: Equivalence Relations, Less-Than and Greater-Than Relations, and Units.Catherine Sophian - 2008 - Behavioral and Brain Sciences 31 (6):670-671.
    Infants' knowledge need not have the same structure as the mature knowledge that develops from it. Fundamental to an understanding of number are concepts of equivalence and less-than and greater-than relations. These concepts, together with the concept of unit, are posited to be the starting points for the development of numerical knowledge.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  48.  18
    Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction.Demetra Christopoulou - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):35-47.
    This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  49.  62
    Residuated Lattices Arising From Equivalence Relations on Boolean and Brouwerian Algebras.Thomas Vetterlein - 2008 - Mathematical Logic Quarterly 54 (4):350-367.
    Logics designed to deal with vague statements typically allow algebraic semantics such that propositions are interpreted by elements of residuated lattices. The structure of these algebras is in general still unknown, and in the cases that a detailed description is available, to understand its significance for logics can be difficult. So the question seems interesting under which circumstances residuated lattices arise from simpler algebras in some natural way. A possible construction is described in this paper.Namely, we consider pairs consisting of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  50.  48
    Equivalence of Consequence Relations: An Order-Theoretic and Categorical Perspective.Nikolaos Galatos & Constantine Tsinakis - 2009 - Journal of Symbolic Logic 74 (3):780-810.
    Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
1 — 50 / 1000