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We extend the construction of a global square sequence in extender models from Zeman  to a construction of coherent non-threadable sequences and give a characterization of stationary reflection at inaccessibles similar to Jensen’s characterization in L.
In Hájek et al. (J Symb Logic 65(2):669–682, 2000) the authors introduce the concept of supersound logic, proving that first-order Gödel logic enjoys this property, whilst first-order Łukasiewicz and product logics do not; in Hájek and Shepherdson (Ann Pure Appl Logic 109(1–2):65–69, 2001) this...
A pool resolution proof is a dag-like resolution proof which admits a depth-first traversal tree in which no variable is used as a resolution variable twice on any branch. The problem of determining whether a given dag-like resolution proof is a valid pool resolution proof is shown to be...
It is relatively consistent with the existence of two supercompact cardinals that a special Aronszajn tree of height
is introduced by a cofinality-preserving forcing of size
A complete Boolean algebra
iff each sequence x in
has a subsequence y such that the equality lim sup z
= lim sup y
holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori...
Pseudo-BCK-algebras are a non-commutative generalization of well-known BCK-algebras. The paper describes a situation when a linearly ordered pseudo-BCK-algebra is an ordinal sum of linearly ordered cone algebras. In addition, we present two identities giving such a possibility of the...
We show that Gitik’s short extender gap-2 forcing is of Prikry type.
For a centerless group G, we can define its automorphism tower. We define G
0 = G, G
α+1 = Aut(G
) and for limit ordinals
. Let τ
be the ordinal when the sequence stabilizes. Thomas’ celebrated theorem says...
We present some natural examples of countable Borel equivalence relations E, F with E ≤
F such that there does not exist a continuous reduction from E to F.
In this paper, we explore some of the consequences of Martin’s Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that...
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