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The Ramsey property implies no mad families. [PDF]
Proc Natl Acad Sci U S A, 2019 We show that if all collections of infinite subsets of $\N$ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing problem going back to Mathias \cite{mathias}.
Schrittesser D, Törnquist A.
europepmc +4 more sources
The axiom of real Blackwell determinacy [PDF]
Archive for Mathematical Logic, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ikegami, D., de Kloet, D., Löwe, B.
openaire +6 more sources
A model of the Axiom of Determinacy in which every set of reals is universally Baire
Forum of Mathematics, SigmaThe consistency of the theory $\mathsf {ZF} + \mathsf {AD}_{\mathbb {R}} + {}$ ‘every set of reals is universally Baire’ is proved relative to $\mathsf {ZFC} + {}$ ‘there is a cardinal that is a limit of Woodin cardinals and of strong ...
Paul B. Larson +2 more
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A Functional (Monadic) Second-Order Theory of Infinite Trees [PDF]
Logical Methods in Computer Science, 2020 This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the ...
Anupam Das, Colin Riba
doaj +1 more source
Countable ordinals and the analytical hierarchy, I [PDF]
, 1975 The following results are proved, using the axiom of Projective Determinacy: (i) For n ≥ 1, every II(1/2n+1) set of countable ordinals contains a Δ(1/2n+1) ordinal, (ii) For n ≥ 1, the set of reals Δ(1/2n) in an ordinal is equal to the largest countable ...
Kechris, A. S.
core +2 more sources
Infinite sequential Nash equilibrium [PDF]
, 2013 In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn.
Roux, Stephane Le
core +1 more source
The Determinacy of Context-Free Games [PDF]
, 2011 We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption.
Equipe De Logique Mathématique +1 more
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When Can We Answer Queries Using Result-Bounded Data Interfaces? [PDF]
, 2018 We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g ...
Amarilli, Antoine, Benedikt, Michael
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism [PDF]
, 2019 This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras.
A Baltag +45 more
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Bad Wadge-like reducibilities on the Baire space [PDF]
, 2013 We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions ...
Ros, Luca Motto
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