Structural Properties of T-λ-Spherical Completions of O-Minimal Fields
The paper establishes structural results for T-λ-spherical completions of models of T-convex o-minimal fields, including that such completions can be embedded in a natural way into certain Hahn field expansions.
실수 순서의 보렐 단일 이론은 결정가능하다
실수 순서의 보렐 집합에 대한 단일 이론은 결정가능하다. 또한 Fσ-집합의 불리언 조합은 보렐 집합의 원소 구조를 형성한다.
The Decidability of the Borel Monadic Theory of Order
The monadic theory of the real numbers (R, ≤) with quantification restricted to Borel sets is decidable. The Boolean combinations of Fσ-sets form an elementary substructure of the Borel sets.
Analyzing Weak A2 Spaces, the Kastanas Game, and Strategically Ramsey Sets
The paper introduces the notion of a weak A2 space (wA2-space), which generalizes spaces satisfying Todorčević's axioms A1-A4 and countable vector spaces. It shows that in any Polish wA2-space, analytic sets are Kastanas Ramsey, and discusses the relationship between Kastanas Ramsey sets and the projective hierarchy. It also shows that in all spaces satisfying A1-A4, every subset of R is Kastanas Ramsey if and only if it is Ramsey. Finally, it shows that in the setting of Gowers wA2-spaces, Kastanas Ramsey sets and strategically Ramsey sets coincide.
Constructive and Intuitionistic Variants of the Modal Logic KB Coincide
The constructive and intuitionistic variants of the modal logic KB coincide, in contrast to the constructive and intuitionistic variants of K which do not prove the same diamond-free formulas.
Game Semantics for the Constructive Modal μ-Calculus
The constructive μ-calculus can be given a game semantics that is equivalent to its bi-relational Kripke semantics. This game semantics can be used to study the properties of the constructive μ-calculus, such as its collapse to modal logic over the intuitionistic modal logic IS5.
完整的跳過自由守護Kleene代數測試推論系統
本文提出了一個完整的代數公理系統,用於描述跳過自由的守護Kleene代數測試(skip-free guarded Kleene algebra with tests, GKAT)表達式的等價性,在語義和雙模擬(bisimulation)兩個層面上都是完備的。
A Complete Algebraic Axiomatization for Skip-free Guarded Kleene Algebra with Tests
The paper presents a complete algebraic axiomatization for the skip-free fragment of Guarded Kleene Algebra with Tests (GKAT), which can be used to reason efficiently about deterministic imperative programs. The axiomatization avoids the need for the previously proposed uniqueness axiom and the non-algebraic side condition, enabling purely algebraic reasoning.
Expressing Counting and Pnueli Modalities in Timed Logics
The core message of this paper is that the counting modalities C^k_I and the Pnueli modalities P^k_I, which specify the existence of a sequence of events within a given time interval I, can be expressed in the Extended Metric Interval Temporal Logic (EMITL) and its fragments, even when I is an arbitrary non-singular interval.
Constructing Permutation Models of Second-Order Predicate Logic with Henkin Interpretation
The Fraenkel-Mostowski-Specker-Asser method can be used to construct permutation models of second-order predicate logic with Henkin interpretation, which allows investigating the strength of second-order principles of choice.
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