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Here we deal with some problems posed by Matet. The first section deals with the existence of stationary subsets of [λ]<κ with no unbounded subsets which are not stationary, where, of course, κ is regular uncountable ≤λ. In the second section we deal with the existence of such clubs. The proofs...
We construct by diagonalization a non-well-founded primitive recursive tree, which is well-founded for co-r.e. sets, provable in Σ1
0. It follows that the supremum of order-types of primitive recursive well-orderings, whose well-foundedness on co-r.e. sets is provable in Σ1
0, equals the limit...
Say that a d.c.e. degree d is isolated by a c.e. degree b, if b
As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of...
In this paper we present two consistency results concerning the existence of large strong measure zero and strongly meager sets.
RID=""ID="" Mathematics Subject Classification (2000): 03E35 RID=""ID="" The first author was supported by Alexander von Humboldt Foundation and NSF...
In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of such sets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely...
We investigate the polynomial time isomorphic type structure of
(the class of tally, polynomial time computable sets). We partition P
into six parts: D
, C, S, F, F^, and study their p-isomorphic properties separately. The structures of
are obvious, where F, F^,...
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