12 citations · 22 across the 7 of their papers we have counts for
14 papers
On the inevitability of the consistency operator
Antonio Montalbán, James Walsh
We examine recursive monotonic functions on the Lindenbaum algebra of . We prove that no such function sends every consistent to a sentence with deductive strength…
Borel Functors and Infinitary Interpretations
Matthew Harrison-Trainor, Russell Miller, Antonio Montalbán
We introduce the notion of infinitary interpretation of structures. In general, an interpretation between structures induces a continuous homomorphism between their automorphism gr…
A mathematical analysis of the evolutionary benefits of sexual reproduction
Andrew Lewis-Pye, Antonio Montalban
The question as to why most higher organisms reproduce sexually has remained open despite extensive research, and has been called "the queen of problems in evolutionary biology". T…
Computable functors and effective interpretability
Matthew Harrison-Trainor, Alexander Melnikov, Russell Miller +1
Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theo…
Independence in computable algebra
Matthew Harrison-Trainor, Alexander Melnikov, Antonio Montalbán
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply…
Computable structures in generic extensions
Julia Knight, Antonio Montalban, Noah Schweber
In this paper, we investigate connections between structures present in every generic extension of the universe and computability theory. We introduce the notion of {\em generi…