Search results for 's4 axiom' (try it on Scholar)

1000+ found
Order:
  1. Susanne Bobzien (2012). If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom. In B. Morison K. Ierodiakonou (ed.), Episteme, etc. OUP UK
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  2.  9
    Timothy Williamson (1995). Does Assertibility Satisfy the S4 Axiom? Critica 27 (81):3 - 25.
    N. B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  3.  1
    R. I. Goldblatt (1973). Concerning the Proper Axiom for $S4.04$ and Some Related Systems. Notre Dame Journal of Formal Logic 14 (3):392-396.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  4.  3
    Leo Simons (1962). A Reduction in the Number of Independent Axiom Schemata for $S4$. Notre Dame Journal of Formal Logic 3 (4):256-258.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  5.  1
    Naoto Yonemitsu (1967). Review: Leo Simons, A Reduction in the Number of Independent Axiom Schemata for S4. [REVIEW] Journal of Symbolic Logic 32 (2):245-245.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  6. R. I. Goldblatt (1975). Erratum: ``Concerning the Proper Axiom for $S4.04$ and Some Related Systems''. Notre Dame Journal of Formal Logic 16 (4):608-608.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  7. Thomas Mormann, McKinsey Algebras and Topological Models of S4.1.
    The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be used to (...)
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  8.  18
    Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos (2002). Shortest Axiomatizations of Implicational S4 and S. Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  9.  25
    Branden Fitelson (2002). Shortest Axiomatizations of Implicational S4 and S5. Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the strict implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  10. Alan Sidelle (2009). Conventionalism and the Contingency of Conventions. Noûs 43 (2):224-241.
    One common objection to Conventionalism about modality is that since it is contingent what our conventions are, the modal facts themselves will thereby be contingent. A standard reply is that Conventionalists can accept this, if they reject the S4 axiom, that what is possibly possible is possible. I first argue that this reply is inadequate, but then continue to argue that it is not needed, because the Conventionalist need not concede that the contingency of our conventions has any bearing (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  11.  4
    José M. Méndez & Gemma Robles (2007). Relevance Logics, Paradoxes of Consistency and the K Rule II. A Non-Constructive Negation. Logic and Logical Philosophy 15 (3):175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  12.  9
    Timothy Williamson (1991). An Alternative Rule of Disjunction in Modal Logic. Notre Dame Journal of Formal Logic 33 (1):89-100.
    Lemmon and Scott introduced the notion of a modal system's providing the rule of disjunction. No consistent normal extension of KB provides this rule. An alternative rule is defined, which KDB, KTB, and other systems are shown to provide, while K and other systems provide the Lemmon-Scott rule but not the alternative rule. If S provides the alternative rule then either —A is a theorem of S or A is whenever A -> ΠA is a theorem; the converse fails. It (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  13. José Méndez & Gemma Robles (2006). Relevance Logics, Paradoxes Of Consistency And The K Rule Ii. Logic and Logical Philosophy 15:175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. Wedefine the logics BK+ and BK′+ by adding to B+ the K rule and to BK+the characteristic S4 axiom, respectively. These logics are endowed witha relatively strong non-constructive negation. We prove that all the logicsdefined lack the K axiom and the standard paradoxes of consistency.
     
    Export citation  
     
    My bibliography  
  14.  50
    John Corcoran (2014). Formalizing Euclid’s First Axiom. Bulletin of Symbolic Logic 20:404-405.
    Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: (...)
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  15. Lee Walters (2014). The Possibility of Unicorns and Modal Logic. Analytic Philosophy 55 (2):295-305.
    Michael Dummett argues, against Saul Kripke, that there could have been unicorns. He then claims that this possibility shows that the logic of metaphysical modality is not S5, and, in particular, that the B axiom is false. Dummett’s argument against B, however, is invalid. I show that although there are number of ways to repair Dummett’s argument against B, each requires a controversial metaphysical or semantic commitment, and that, regardless of this, the case against B is undermotivated. Dummett’s case (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  16.  25
    Melvin Fitting (2008). A Quantified Logic of Evidence. Annals of Pure and Applied Logic 152 (1):67-83.
    A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  17.  55
    M. Rathjen (2001). Kripke-Platek Set Theory and the Anti-Foundation Axiom. Mathematical Logic Quarterly 47 (4):435-440.
    The paper investigates the strength of the Anti-Foundation Axiom, AFA, on the basis of Kripke-Platek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  18. Olivier Esser (2000). Inconsistency of the Axiom of Choice with the Positive Theory GPK+ ∞. Journal of Symbolic Logic 65 (4):1911 - 1916.
    The idea of the positive theory is to avoid the Russell's paradox by postulating an axiom scheme of comprehension for formulas without "too much" negations. In this paper, we show that the axiom of choice is inconsistent with the positive theory GPK + ∞.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  19.  15
    W. J. Blok (1980). The Lattice of Modal Logics: An Algebraic Investigation. Journal of Symbolic Logic 45 (2):221-236.
    Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   17 citations  
  20.  1
    F. Wolter, H. Wansing, M. de Rijke & M. Zakharyaschev, Advances in Modal Logic, Volume.
    We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a £ϕ → £ aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation a. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the (...)
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography   2 citations  
  21. Peter Nyikos & Leszek Piątkiewicz (1995). On the Equivalence of Certain Consequences of the Proper Forcing Axiom. Journal of Symbolic Logic 60 (2):431-443.
    We prove that a number of axioms, each a consequence of PFA (the Proper Forcing Axiom) are equivalent. In particular we show that TOP (the Thinning-out Principle as introduced by Baumgartner in the Handbook of set-theoretic topology), is equivalent to the following statement: If I is an ideal on ω 1 with ω 1 generators, then there exists an uncountable $X \subseteq \omega_1$ , such that either [ X] ω ∩ I = ⊘ or $\lbrack X\rbrack^\omega \subseteq I$.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  22.  10
    Paul Corazza (2000). Consistency of V = HOD with the Wholeness Axiom. Archive for Mathematical Logic 39 (3):219-226.
    The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language $\{\in,j\}$ , and that asserts the existence of a nontrivial elementary embedding $j:V\to V$ . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an $I_1$ embedding. This answers (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  23.  12
    Samir Chopra, Aditya Ghose, Thomas Meyer & Ka-Shu Wong (2008). Iterated Belief Change and the Recovery Axiom. Journal of Philosophical Logic 37 (5):501 - 520.
    The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  24.  9
    Arthur W. Apter (2011). Indestructibility, HOD, and the Ground Axiom. Mathematical Logic Quarterly 57 (3):261-265.
    Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, …, 4 are the theories “ZFC + φ1 + φ2,” “ZFC + ¬φ1 + φ2,” “ZFC + φ1 + ¬φ2,” and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, …, 4, Ai = df{δ κ is inaccessible. We show it is (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  25.  10
    Thilo Weinert (2010). The Bounded Axiom A Forcing Axiom. Mathematical Logic Quarterly 56 (6):659-665.
    We introduce the Bounded Axiom A Forcing Axiom . It turns out that it is equiconsistent with the existence of a regular ∑2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  26.  14
    Wolfgang Rautenberg (1976). Some Properties of the Hierarchy of Modal Logics (Preliminary Report). Bulletin of the Section of Logic 5 (3):103-104.
    We are concerned with modal logics in the class EM0 of extensions of M0 . G denotes re exive frames. MG the modal logic on G in the sense of Kripke. M is nite if M = MG for some nite G. Finite G's will be drawn as framed diagrams, e.g. G = ! ; G = ! ; the latter shorter denoted by . EM0 is a complete lattice with zero M0 and one M . If M M0 M0 (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  27.  13
    Teruyuki Yorioka (2008). Some Weak Fragments of Martin's Axiom Related to the Rectangle Refining Property. Archive for Mathematical Logic 47 (1):79-90.
    We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  28.  3
    Robert S. Lubarsky & Michael Rathjen (2003). On the Regular Extension Axiom and its Variants. Mathematical Logic Quarterly 49 (5):511.
    The regular extension axiom, REA, was first considered by Peter Aczel in the context of Constructive Zermelo-Fraenkel Set Theory as an axiom that ensures the existence of many inductively defined sets. REA has several natural variants. In this note we gather together metamathematical results about these variants from the point of view of both classical and constructive set theory.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  29.  4
    Victor Pambuccian (2010). Forms of the Pasch Axiom in Ordered Geometry. Mathematical Logic Quarterly 56 (1):29-34.
    We prove that, in the framework of ordered geometry, the inner form of the Pasch axiom does not imply its outer form . We also show that OP can be properly split into IP and the weak Pasch axiom.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  30.  13
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Eleftherios Tachtsis (2005). Properties of the Real Line and Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 51 (6):598-609.
    We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  31.  5
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Metric Spaces and the Axiom of Choice. Mathematical Logic Quarterly 49 (5):455-466.
    We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  32.  4
    Paul Howard (2007). Bases, Spanning Sets, and the Axiom of Choice. Mathematical Logic Quarterly 53 (3):247-254.
    Two theorems are proved: First that the statement“there exists a field F such that for every vector space over F, every generating set contains a basis”implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ℤ2 has a basis implies that every well-ordered collection of two-element sets has a choice function.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  33.  66
    John Bell (2008). The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories. Mathematical Logic Quarterly 54 (2):194-201.
    A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  34.  8
    K. Keremedis (2001). The Vector Space Kinna-Wagner Principle is Equivalent to the Axiom of Choice. Mathematical Logic Quarterly 47 (2):205-210.
    We show that the axiom of choice AC is equivalent to the Vector Space Kinna-Wagner Principle, i.e., the assertion: “For every family [MATHEMATICAL SCRIPT CAPITAL V]= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fiis a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that every (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  35.  26
    Gemma Robles & José M. Méndez (2014). Curry's Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Studia Logica 102 (1):185-217.
    “Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  36.  6
    G. Gutierres (2003). Sequential Topological Conditions in &Unknown; in the Absence of the Axiom of Choice. Mathematical Logic Quarterly 49 (3):293.
    It is known that – assuming the axiom of choice – for subsets A of ℝ the following hold: A is compact iff it is sequentially compact, A is complete iff it is closed in ℝ, ℝ is a sequential space. We will show that these assertions are not provable in the absence of the axiom of choice, and that they are equivalent to each.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  37.  14
    Larisa Maksimova (2002). Complexity of Interpolation and Related Problems in Positive Calculi. Journal of Symbolic Logic 67 (1):397-408.
    We consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity, and interpolation problems over the intuitionistic logic Int and (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  38.  8
    Olivier Esser (2003). On the Axiom of Extensionality in the Positive Set Theory. Mathematical Logic Quarterly 49 (1):97-100.
    This is a study of the relative interpretability of the axiom of extensionality in the positive set theory. This work has to be considered in the line of works of R. O. Gandy, D. Scott and R. Hinnion who have studied the relative interpretability of the axiom of extensionality in set theories of Zermelo and Zermelo-Fraenkel.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  39.  8
    Edwin D. Mares & Robert K. Meyer (1993). The Semantics Ofr. Journal of Philosophical Logic 22 (1):95 - 110.
    The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  40.  12
    Stefano Baratella & Ruggero Ferro (1993). A Theory of Sets with the Negation of the Axiom of Infinity. Mathematical Logic Quarterly 39 (1):338-352.
    In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  41.  5
    Kyriakos Keremedis (1998). Extending Independent Sets to Bases and the Axiom of Choice. Mathematical Logic Quarterly 44 (1):92-98.
    We show that the both assertions “in every vector space B over a finite element field every subspace V ⊆ B has a complementary subspace S” and “for every family [MATHEMATICAL SCRIPT CAPITAL A] of disjoint odd sized sets there exists a subfamily ℱ={Fj:j ϵω} with a choice function” together imply the axiom of choice AC. We also show that AC is equivalent to the statement “in every vector space over ℚ every generating set includes a basis”.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  42.  4
    J. Brendle (2000). Martin's Axiom and the Dual Distributivity Number. Mathematical Logic Quarterly 46 (2):241-248.
    We show that it is consistent that Martin's axiom holds, the continuum is large, and yet the dual distributivity number ℌ is κ1. This answers a question of Halbeisen.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  43.  11
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Products of Compact Spaces and the Axiom of Choice II. Mathematical Logic Quarterly 49 (1):57-71.
    This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  44.  9
    Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2008). Unions and the Axiom of Choice. Mathematical Logic Quarterly 54 (6):652-665.
    We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  45.  10
    Juliette Dodu & Marianne Morillon (1999). The Hahn-Banach Property and the Axiom of Choice. Mathematical Logic Quarterly 45 (3):299-314.
    We work in set theory ZF without axiom of choice. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gateaux-differentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f: F → ℝ is a linear functional such that f ≤ p|F then there exists a linear functional g : E → ℝ such that g (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  46.  39
    David W. Miller (2007). Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice. Logica Universalis 1 (1):183-199.
    . Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  47.  8
    Kyriakos Keremedis (2001). Disasters in Topology Without the Axiom of Choice. Archive for Mathematical Logic 40 (8):569-580.
    We show that some well known theorems in topology may not be true without the axiom of choice.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  48.  30
    Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. Bulletin of Symbolic Logic 16 (1):37-84.
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  49.  9
    Norbert Brunner & H. Reiju Mihara (2000). Arrow's Theorem, Weglorz' Models and the Axiom of Choice. Mathematical Logic Quarterly 46 (3):335-359.
    Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow-type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  50.  9
    E. Tachtsis & K. Keremedis (2001). Compact Metric Spaces and Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 47 (1):117-128.
    It is shown that for compact metric spaces the following statements are pairwise equivalent: “X is Loeb”, “X is separable”, “X has a we ordered dense subset”, “X is second countable”, and “X has a dense set G = ∪{Gn : n ∈ ω}, ∣Gn∣ < ω, with limn→∞ diam = 0”. Further, it is shown that the statement: “Compact metric spaces are weakly Loeb” is not provable in ZF0 , the Zermelo-Fraenkel set theory without the axiom of regularity, (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
1 — 50 / 1000