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- Matthew Harrison-Trainor, JACK KLYS, Rahim Moosa
- 2011

Motivated by the problem of the existence of bounds on degrees and orders in checking primality of radical (partial) differential ideals, the nonstandard methods of van den Dries and Schmidt [“Bounds… (More)

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the… (More)

- Matthew Harrison-Trainor, Wesley H. Holliday, Thomas F. Icard
- Mathematical Social Sciences
- 2018

The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal… (More)

We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank ωCK 1 , the computable infinitary theory is א0-categorical. Millar and… (More)

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 the condition to… (More)

- Matthew Harrison-Trainor
- Ann. Pure Appl. Logic
- 2017

A set A is coarsely computable with density r ∈ [0,1] if there is an algorithm for deciding membership in A which always gives a (possibly incorrect) answer, and which gives a correct answer with… (More)

This paper builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by… (More)

- Matthew Harrison-Trainor, Alexander Melnikov, Russell G. Miller, Antonio Montalbán
- J. Symb. Log.
- 2017

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 theory, and the other… (More)

The Scott rank of a countable structure is a measure, coming from the proof of Scott’s isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a… (More)

- Barbara F. Csima, Matthew Harrison-Trainor
- J. Symb. Log.
- 2017

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of… (More)