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On the computability-theoretic complexity of trivial, strongly minimal models
computability-theoretic strongly minimal models
2015/9/28
We show the existence of a trivial, strongly minimal (and thus
uncountably categorical) theory for which the prime model is computable and
each of the other countable models computes 0
00. This res...
Game arguments in computability theory and algorithmic information theory
Game arguments computability theory algorithmic information theory Logic
2012/4/17
We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional ...
A subset of {1,2,3,...}^n whose non-computability leads to the existence of a Diophantine equation whose solvability is logically undecidable
Hilbert’s Tenth Problem logically undecidable Diophantine equation Logic
2011/9/22
Abstract: Let B(n)={(x_1,...,x_n) \in {1,2,3,...}^n: for each positive integers y_1,...,y_n the conjunction
(\forall i,j,k \in {1,...,n} (x_i+x_j=x_k ==> y_i+y_j=y_k)) AND
\forall i,j,k \in {1,......
A computability challenge: asymptotic bounds and isolated error-correcting codes
asymptotic bounds isolated error-correcting codes Information Theory
2011/9/16
Abstract: Consider the set of all error--correcting block codes over a fixed alphabet with $q$ letters. It determines a recursively enumerable set of points in the unit square with coordinates $(R,\de...
Brolin-Lyubich measure R of a rational endomorphism R : ˆC !ˆC with deg R 2 is the unique invariant measure of maximal entropy hR =htop(R) = log d.