APAL
2004
14 years 9 days ago
2004
We investigate the initial segment complexity of random reals. Let K( ) denote pre
APAL
2004
14 years 9 days ago
2004
Modus ponens provides the central theme. There are laws, of the form A C. A logic (or other theory) L collects such laws. Any datum A (or theory T incorporating such data) provid...
APAL
2004
14 years 9 days ago
2004
The classical Feferman
APAL
2004
14 years 9 days ago
2004
Relation were invented by Tarski and his collaborators in the middle of the twentieth century. The concept of integrality arose naturally early in the history of the subject, and s...
APAL
2004
14 years 9 days ago
2004
We study the relationship between least and inflationary fixed-point logic. In 1986, Gurevich and Shelah proved that in the restriction to finite structures, the two logics have t...
APAL
2004
14 years 9 days ago
2004
Gaifman's normal form theorem showed that every first order sentence of quantifier rank n is equivalent to a Boolean combination of "scattered local sentences", whe...
APAL
2004
14 years 9 days ago
2004
We study the extension (introduced as BT in [5]) of the theory S1 2 by instances of the dual (onto) weak pigeonhole principle for p-time functions, dWPHP(PV )x x2 . We propose a n...
APAL
2004
14 years 9 days ago
2004
The purpose of this article is to present a new theory IPA() for fixed points over arithmetic which allows the building up of fixed points in a very nested and entangled way. But ...
APAL
2004
14 years 9 days ago
2004
The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower...
APAL
2004
14 years 9 days ago
2004
First-order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently several se...