21 found
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  1.  4
    Separating Principles Below Ramsey's Theorem for Pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
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  2.  12
    Ultrafilters in Reverse Mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.
  3.  24
    Epsilon Substitution for Transfinite Induction.Henry Towsner - 2004 - Archive for Mathematical Logic 44 (4):397-412.
    We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.
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  4.  12
    A Simple Proof and Some Difficult Examples for Hindman's Theorem.Henry Towsner - 2012 - Notre Dame Journal of Formal Logic 53 (1):53-65.
    We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several examples of colorings of the integers which do not have computable witnesses to Hindman's Theorem.
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  5.  16
    Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic.Henry Towsner - 2011 - Journal of Symbolic Logic 76 (1):353 - 360.
    Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.
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  6.  36
    Functional Interpretation and Inductive Definitions.Jeremy Avigad & Henry Towsner - 2009 - Journal of Symbolic Logic 74 (4):1100-1120.
    Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.
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  7.  5
    Relatively Exchangeable Structures.Harry Crane & Henry Towsner - 2018 - Journal of Symbolic Logic 83 (2):416-442.
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  8.  7
    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).
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  9.  2
    Epsilon Substitution for $$\Textit{ID}_1$$ ID 1 Via Cut-Elimination.Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):497-531.
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  10.  14
    Infinitary Methods in Finite Model Theory. [REVIEW]Scott Weinstein, Henry Towsner & Steven Lindell - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 305-318.
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  11.  12
    Partial Impredicativity in Reverse Mathematics.Henry Towsner - 2013 - Journal of Symbolic Logic 78 (2):459-488.
    In reverse mathematics, it is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on how to weaken the assumption while preserving the conclusion (other than reducing all the way to the tautology of assuming the conclusion). A main cause of this phenomenon is the proof of a $\Pi^1_2$ sentence from the theory $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$. Using methods based on the functional interpretation, we introduce a family of weakenings of $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$ (...)
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  12.  10
    A Realizability Interpretation for Classical Analysis.Henry Towsner - 2004 - Archive for Mathematical Logic 43 (7):891-900.
    We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀x∃yA(x,y), this provides a recursive type 1 function which computes the function given by f(x)=y iff y is the least number such that A(x,y).
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  13.  4
    Separating Principles Below WKL0.Stephen Flood & Henry Towsner - 2016 - Mathematical Logic Quarterly 62 (6):507-529.
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  14.  9
    New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011.Jeremy Avigad, Ulrich W. Kohlenbach, Henry Towsner, Samson Abramsky, Andreas Blass, Larry Moss, Alf Onshuus Nino, Patrick Speissegger, Juris Steprans & Monica VanDieren - 2012 - Bulletin of Symbolic Logic 18 (1).
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  15.  5
    Antonio Montalbán, Indecomposable Linear Orderings and Hyperarithmetic Analysis. Journal of Mathematical Logic, Vol. 6 , No. 1, Pp. 89–120. - Itay Neeman, The Strength of Jullien’s Indecomposability Theorem. Journal of Mathematical Logic, Vol. 8 , No. 1, Pp. 93–119. - Itay Neeman, Necessary Use Ofinduction in a Reversal. Journal of Symbolic Logic, Vol. 76 , No. 2, Pp. 561–574. [REVIEW]Henry Towsner - 2014 - Bulletin of Symbolic Logic 20 (3):366-368.
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  16.  2
    Epsilon Substitution for $$Textit{ID}_1$$ Via Cut-Elimination.Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):497-531.
    The \-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory \ using a variant of the cut-elimination formalism introduced by Mints.
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  17.  6
    2010 North American Annual Meeting of the Association for Symbolic Logic.Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.
  18.  4
    Edinburgh, Scotland July 1–4, 2008.Olivier Danvy, Anuj Dawar, Makoto Kanazawa, Sam Lomonaco, Mark Steedman, Henry Towsner & Nikolay Vereshchagin - 2008 - Bulletin of Symbolic Logic 14 (4).
  19.  5
    Ordinal Analysis by Transformations.Henry Towsner - 2009 - Annals of Pure and Applied Logic 157 (2-3):269-280.
    The technique of using infinitary rules in an ordinal analysis has been one of the most productive developments in ordinal analysis. Unfortunately, one of the most advanced variants, the Buchholz Ωμ rule, does not apply to systems much stronger than -comprehension. In this paper, we propose a new extension of the Ω rule using game-theoretic quantifiers. We apply this to a system of inductive definitions with at least the strength of a recursively inaccessible ordinal.
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  20.  3
    Dividing and Weak Quasi-Dimensions in Arbitrary Theories.Isaac Goldbring & Henry Towsner - 2015 - Archive for Mathematical Logic 54 (7-8):915-920.
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  21. Metastability in the Furstenberg-Zimmer Tower.Jeremy Avigad & Henry Towsner - unknown
    According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemer\'edi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength (...)
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