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AML
2011
221views Mathematics» more  AML 2011»
7 years 11 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
190views Mathematics» more  AML 2011»
7 years 11 months ago
Topological aspects of the Medvedev lattice
We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated ...
Andrew E. M. Lewis, Richard A. Shore, Andrea Sorbi
AML
2011
177views Mathematics» more  AML 2011»
8 years 2 months ago
A superhigh diamond in the c.e. tt-degrees
The notion of superhigh computably enumerable (c.e.) degrees was first introduced by Mohrherr in [7], where she proved the existence of incomplete superhigh c.e. degrees, and high...
Douglas Cenzer, Johanna N. Y. Franklin, Jiang Liu ...
AML
2011
322views Mathematics» more  AML 2011»
8 years 2 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
204views Mathematics» more  AML 2011»
8 years 2 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
AML
2011
204views Mathematics» more  AML 2011»
8 years 2 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
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