Related papers: The Provably Total Set-Recursive Functions of KPl

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.

We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…

We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…

Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…

We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show…

We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness…

For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…

We survey old and recent results on the problem of finding a complete set of rules describing the behavior of the power function, i.e. the function which takes a cardinal $\kappa$ to the cardinality of its power $2^\kappa$.

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

In the lecture notes it is shown that an ordinal $\psi_{\Omega}(\varepsilon_{\mathbb{S}^{+}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$. In this note we show that ${\sf…

In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…

We provide a version of the celebrated theorem of Koml\'os in which, rather then random quantities, a sequence of finitely additive measures is considered. We obtain a form of the subsequence principle and some applications.

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for…

We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an…

Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…

We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…