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AML
2011
322views Mathematics» more  AML 2011»
10 years 6 months ago
A dedekind finite borel set
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2ω is a Gδσ-set then either...
Arnold W. Miller
AML
2011
221views Mathematics» more  AML 2011»
10 years 3 months ago
A remark on the tree property in a choiceless context
We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree prope...
Arthur W. Apter
AML
2011
204views Mathematics» more  AML 2011»
10 years 6 months ago
A note on propositional proof complexity of some Ramsey-type statements
Any valid Ramsey statement n −→ (k)2 2 can be encoded into a DNF formula RAM(n, k) of size O(nk) and with terms of size k 2 . Let rk be the minimal n for which the statement h...
Jan Krajícek
AML
2011
204views Mathematics» more  AML 2011»
10 years 6 months ago
Intermediate Logics and the de Jongh property
We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property. Dedicated to Petr H´ajek, on the occasion of his...
Dick de Jongh, Rineke Verbrugge, Albert Visser
Mathematics
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