Related papers: Models of $VTC^0$ as exponential integer parts

We prove the correctness of the AKS algorithm \cite{AKS} within the bounded arithmetic theory $T^{count}_2$ or, equivalently, the first-order consequences of the theory $VTC^0$ expanded by the smash function, which we denote by $VTC^0_2$.…

We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal $\alpha$ there exists an ordinal $\beta$ such that $1+\beta\cdot(\beta+\alpha)$ (ordinal arithmetic) admits an…

The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a…

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way.…

We present and analyze a natural hierarchy of weak theories, develop analysis in them, and show that they are interpretable in bounded quantifier arithmetic $\text{I}\Delta_0$ (and hence in Robinson arithmetic Q). The strongest theories…

We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our…

I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…

We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the…

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

We study uncountable structures similar to the Fra\"iss\'e limits. The standard inductive arguments from the Fra\"iss\'e theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In…

Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…

We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to…

We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the domain of our interpretation is definable in the group.

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…

Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…