Measure theory and higher order arithmetic

On Higher Arithmetic Intersection Theory

Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo

Deduction modulo is a paradigm which consists in applying the inference rules of a deductive system—such as for instance natural deduction—modulo a rewrite system over terms and propositions. It has been shown that higher-order logic can be simulated into the first-order natural deduction modulo. However, a theorem stated by Gödel and proved by Parikh expresses that proofs in second-order arith...

Harrington's Principle in Higher order Arithmetic

Let Z2, Z3, and Z4 denote 2nd, 3rd, and 4th order arithmetic, respectively. We let Harrington’s Principle, HP, denote the statement that there is a real x such that every x–admissible ordinal is a cardinal in L. The known proofs of Harrington’s theorem “Det(Σ1) implies 0 ] exists” are done in two steps: first show that Det(Σ1) implies HP, and then show that HP implies 0] exists. The first step ...

Higher order cohomology of arithmetic groups

Higher order cohomology of arithmetic groups is expressed in terms of (g, K)-cohomology. It is shown that the latter can be computed using functions of moderate growth. Higher order versions of results of Borel are proven and the Borel conjecture in the higher order setting is stated.

Higher-Order Game Theory

In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not exist. In this paper we introduce a representation of games where players’ goals are modeled based on so-called higher-order functions. Our representation provi...