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A note on Gentzen’s ordinal assignment
Springer Science and Business Media LLC - Tập 58 - Trang 347-352 - 2018
Annika Kanckos
Gentzen’s height measure of the 1938 consistency proof is a cumulative complexity measure for sequents that is measured bottom-up in a derivation. By a factorisation of the ordinal assignment a top-down ordinal assignment can be given that does not depend on information occurring below the sequent to which the ordinal is assigned. Furthermore, an ordinal collapsing function is defined in order to ... hiện toàn bộ
Some definable properties of sets in non-valuational weakly o-minimal structures
Springer Science and Business Media LLC - Tập 56 - Trang 309-317 - 2017
Somayyeh Tari
Let $${\mathcal {M}}=(M,<,+,\cdot ,\ldots )$$ be a non-valuational weakly o-minimal expansion of a real closed field $$(M,<,+,\cdot )$$ . In this paper, we prove that $${\mathcal {M}}$$ has a $$C^r$$ -strong cell decomposition property, for each positive integer r, a best analogous result from Tanaka and Kawakami (Far East J Math Sci (FJMS) 25(3):417–431, 2007). We also show that curve selection p... hiện toàn bộ
On pairs of free modules over a Dedekind domain
Springer Science and Business Media LLC - - 2005
Saverio Cittadini, Carlo Toffalori
The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an a... hiện toàn bộ
Scott sentences for equivalence structures
Springer Science and Business Media LLC - Tập 59 - Trang 453-460 - 2019
Sara B. Quinn
For a computable structure $${\mathcal {A}}$$, if there is a computable infinitary Scott sentence, then the complexity of this sentence gives an upper bound for the complexity of the index set $$I({\mathcal {A}})$$. If we can also show that $$I({\mathcal {A}})$$ is m-complete at that level, then there is a correspondence between the complexity of the index set and the complexity of a Scott sentenc... hiện toàn bộ
A classification of an iterative hierarchy
Springer Science and Business Media LLC - Tập 23 - Trang 175-186 - 1983
Hans Kleine Büning
Equiconsistencies at subcompact cardinals
Springer Science and Business Media LLC - Tập 55 - Trang 207-238 - 2015
Itay Neeman, John Steel
We present equiconsistency results at the level of subcompact cardinals. Assuming SBH δ , a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □(δ) and □ δ fail, then δ is subcompact in a class inner model. If in addition □(δ +) fails, we prove that δ is $${\Pi_1^2}$$ subcompact in a class inner model. These results are optimal, and lead to equicons... hiện toàn bộ
On injective enumerability of recursively enumerable classes of cofinite sets
Springer Science and Business Media LLC - Tập 34 - Trang 183-196 - 1995
Stephan Wehner
To date the problem of finding a general characterization of injective enumerability of recursively enumerable (r.e) classes of r.e. sets has proved intractable. This paper investigates the problem for r.e. classes of cofinite sets. We state a suitable criterion for r.e. classesC such that there is a boundn∈ω with |ω-A|≤n for allA∈C. On the other hand an example is constructed which shows that Lac... hiện toàn bộ
Souslin algebra embeddings
Springer Science and Business Media LLC - - 2011
Gido Scharfenberger-Fabian
Semi-honest subrecursive degrees and the collection rule in arithmetic
Springer Science and Business Media LLC - Tập 63 - Trang 163-180 - 2023
Andrés Cordón-Franco, F. Félix Lara-Martín
By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentence... hiện toàn bộ
What is so special with the powerset operation?
Springer Science and Business Media LLC - Tập 43 - Trang 723-737 - 2004
Athanassios Tzouvaras
The powerset operator, , is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., | (x)|>|x|. As a consequence of (3), has a proper class as least fixed point (the universe itself). In this paper we address the questions: (a) How does contribute to the generation of the class of all positive operators? (b) Are there othe... hiện toàn bộ
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