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《Annals of Pure and Applied Logic》2023,174(6):103259
We introduce a realisability semantics for infinitary intuitionistic set theory that is based on Ordinal Turing Machines (OTMs). We show that our notion of OTM-realisability is sound with respect to certain systems of infinitary intuitionistic logic, and that all axioms of infinitary Kripke-Platek set theory are realised. Finally, we use a variant of our notion of realisability to show that the propositional admissible rules of (finitary) intuitionistic Kripke-Platek set theory are exactly the admissible rules of intuitionistic propositional logic. 相似文献
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A term rewrite system is called simply terminating if its termination can be shown by means of a simplification ordering. According to a result of Weiermann, the derivation length function of any simply terminating finite rewrite system is eventually dominated by a Hardy function of ordinal less than the small Veblen ordinal. This bound had appeared to be of rather theoretical nature, because all known examples had had multiple recursive complexities, until recently Touzet constructed simply (and even totally) terminating examples with complexities beyond multiple recursion. This was established by simulating the Hydra battle for all ordinal segments below the proof-theoretic ordinal of Peano arithmetic. By extending this result to the small Veblen ordinal we prove the huge bound of Weiermann to be sharp. As a spin-off we can show that total termination allows for complexities as high as those of simple termination.
This paper is part of the authors doctoral dissertation project (under the supervision of Professor A. Weiermann at the University of Münster).The work on this paper was supported by DFG grant WE 2178/2–1
Mathematics Subject Classification (2000): 03D20, 68Q15, 68Q42 相似文献
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Martin Meier 《Israel Journal of Mathematics》2012,192(1):1-58
Type spaces in the sense of Harsanyi (1967/68) play an important role in the theory of games of incomplete information. They can be considered as the probabilistic analog of Kripke structures. By an infinitary propositional language with additional operators “individual i assigns probability at least α to” and infinitary inference rules, we axiomatize the class of (Harsanyi) type spaces. We prove that our axiom system is strongly sound and strongly complete. To the best of our knowledge, this is the very first strong completeness theorem for a probability logic with σ-additive probabilities. We show this by constructing a canonical type space whose states consist of all maximal consistent sets of formulas. Furthermore, we show that this canonical space is universal (i.e., a terminal object in the category of type spaces) and beliefs complete. 相似文献
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Abbas Najati 《Czechoslovak Mathematical Journal》2010,60(2):541-547
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation.
Specially, we conclude that every Jordan triple θ-derivation on a Lie triple system is a θ-derivation. 相似文献
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R. Pliuškevičius 《Journal of Mathematical Sciences》2005,126(3):1210-1228
In the paper, a fragment of first-order linear time logic (with operators next and always) is considered. The object under investigation in this fragment is so-called t-D-sequents. For considered t-D-sequents, an invertible infinitary sequent calculus G
+
is constructed. This calculus has no loop rules, i.e., rules with duplications of the main formula in the premises of the rules. The calculus G
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along with an -type rule for the temporal operator always contains an integrated separation rule (IS), which includes the traditional loop-type rule ( ), a special rule ( ) (without duplication of the main formula), and the traditional rule for the temporal operator next. The rule ( ) is incorporated in an axiom. The soundness and -completeness of the constructed calculus G
+
are proved. Bibliography: 43 titles.Published in Zapiski Nauchnykh Seminarov POMI, Vol.293, 2002, pp. 149–180.This revised version was published online in April 2005 with a corrected cover date and article title. 相似文献
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Isidore Fleischer 《Mathematical Logic Quarterly》1993,39(1):197-200
The present note is a reworking and streamlining of Daigneault and Monk's Representation Theory for Polyadic Algebras. MSC: 03G15. 相似文献
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Jiří Rosický 《Algebra Universalis》1985,20(1):123-126
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W. Calvert S. S. Goncharov J. F. Knight Jessica Millar 《Archive for Mathematical Logic》2009,48(1):25-38
Computable structures of Scott rank are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism,
by a sentence of , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures
with Scott rank whose computable infinitary theories are each -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott
rank , which guarantee that the resulting structure is a model of an -categorical computable infinitary theory.
Work on this paper began at the Workshop on Model Theory and Computable Structure Theory at University of Florida Gainesville,
in February, 2007. The authors are grateful to the organizers of this workshop. They are also grateful for financial support
from National Science Foundation grants DMS DMS 05-32644, DMS 05-5484. The second author is also grateful for the support
of grants RFBR 08-01-00336 and NSc-335.2008.1. 相似文献
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Randall McCutcheon 《Israel Journal of Mathematics》2001,121(1):157-172
A joint extension of H. Furstenberg’s central sets theorem, the Hales-Jewett coloring theorem and the polynomial van der Waerden theorem of V. Bergelson and A. Leibman is obtained by an elaboration on Furstenberg and Y. Katznelson’s approach to infinitary Ramsey theory via the enveloping semigroup. 相似文献
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Stefano Baratella 《Mathematical Logic Quarterly》2015,61(6):448-457
We show how to extend the Continuous Propositional Logic by means of an infinitary rule in order to achieve a Strong Completeness Theorem. Eventually we investigate how to recover a weak version of the Deduction Theorem. 相似文献
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B. E. Johnson 《Transactions of the American Mathematical Society》2001,353(1):313-325
Kadison has shown that local derivations from a von Neumann algebra into any dual bimodule are derivations. In this paper we extend this result to local derivations from any -algebra into any Banach -bimodule . Most of the work is involved with establishing this result when is a commutative -algebra with one self-adjoint generator. A known result of the author about Jordan derivations then completes the argument. We show that these results do not extend to the algebra of continuously differentiable functions on . We also give an automatic continuity result, that is, we show that local derivations on -algebras are continuous even if not assumed a priori to be so.
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Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an –type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set of extralogical axioms). For each system we provide a syntactic proof of cut elimination and a proof of completeness.Supported by MIUR COFIN 02 Teoria dei Modelli e Teoria degli Insiemi, loro interazioni ed applicazioni.Supported by MIUR COFIN 02 PROTOCOLLO.Mathematics Subject Classification (2000):03B22, 03B45, 03F05 相似文献
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Richard H Herman 《Journal of Functional Analysis》1975,20(3):234-239
In this note we discuss various extensions of a normal 1 derivation of a uniformly hyperfinite C1-algebra. Various approximation theorems are employed to show when said extensions generate automorphism groups of the C1-algebra. We characterize the “maximal” extension of Sakai and Powers as a graph limit and show when this extension is the closure of the given derivation. We also discuss an identity obeyed by the resolvent of a derivation. 相似文献
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We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ω( Q u)ω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht‐Fraïssé type game similar to the one in [9]. A consequence is that every sentence of L∞ω( Q u)ω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form (?≥iy)ψ(y), where ψ(y) has counting quantifiers restricted to the (2n–1 – 1)‐neighborhood of y. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Chris Macmeikan 《Indagationes Mathematicae》2004,15(2):257-267
Let G be a connected semi-simple algebraic group over . Fix a maximal torus T in G with coordinate ring T. Let Φ+ be the set of positive roots of G with respect to T. The pair (T, A), where A = {kerα}α?φ+, is a toral arrangement. We show that if G is simply connected then the module of A-derivations D(A) is a free T-module. 相似文献
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