Indeksowane metadane

Lp.
Dublin Core
PKP Metadata Items
Metadane dla dokumentu

1.
Tytuł
Tytuł dokumentu
Reductions between certain incidence problems and the continuum hypothesis

2.
Autor
Imię, nazwisko autora, afiliacja
Samuel G. da Silva; 4

3.
Przedmiot
Słowo(a) kluczowe
Continuum Hypothesis, incidence problems, complexity, Dialectica Categories.

4.
Description
Abstrakt

In this work, we consider two families of incidence problems, C_{1} and C_{2},, which are related to real numbers and countable subsets of the real line. Instances of problems of C_{1} are as follows: given a real number x, pick randomly a countable set of reals A hoping that *x *∈ *A*, whereas instances of problems of C_{2} are as follows: given a countable set of reals A, pick randomly a real number x hoping that *x* ∉ *A*. One could arguably defend that, at least intuitively, problems of C_{2} are easier to solve than problems of C_{1}. After some suitable formalization, we prove (within **ZFC**) that, on one hand, problems of C_{2} are, indeed, at least as easy to solve as problems of C_{1}. On the other hand, the statement “Problems of C_{1} have the exact same complexity of problems of C_{2}” is shown to be an equivalent of the Continuum Hypothesis.

**Received **18 February 2019

**AMS subject classification**: Primary 03E50; Secondary 18A05, 18A15

5.
Wydawca
Organizing agency, location
Uniwersytet Jagielloński

6.
Date
(YYYY-MM-DD)
2019-10-08

7.
Format
Format pliku
PDF

10.
Źródło
Tytuł czasopisma/konferencji; vol., nr. (rok)
Reports on Mathematical Logic; 2019, Number 54 (2019)

11.
Język
English=EN
EN