1 - 6 of 6 articles
We give some restrictions for the search for a model of the club principle with no Souslin trees. We show that
, is almost constant on) together with CH and “all Aronszajn trees are special” is consistent relative to ZFC. This implies the analogous...
We prove two conservation results involving a generalization of the principle of strict
-reflection, in the context of bounded arithmetic. In this context a separation between the concepts of bounded set and binary sequence seems to emerge as fundamental.
Defining the degree of categoricity of a computable structure
to be the least degree d for which
is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above...
We show that there is a computable procedure which, given an ∀∃-sentence
in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether
is true in the Medvedev degrees of
classes in Cantor space,...
We show the non-arithmeticity of 1st order theories of lattices of Σ
sentences modulo provable equivalence in a formal theory, of diagonalizable algebras of a wider class of arithmetic theories than has been previously known, and of the lattice of degrees of interpretability over PA. The first...
Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degrees coincides with the one considered in the
degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in (Ann Pure Appl Log 62(3):207–263, 1993) that there are d.r.e. degrees a, b, c...
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