On countably saturated linear orders and certain class of countably saturated graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00537538" target="_blank" >RIV/67985840:_____/21:00537538 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00153-020-00742-7" target="_blank" >https://doi.org/10.1007/s00153-020-00742-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00153-020-00742-7" target="_blank" >10.1007/s00153-020-00742-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On countably saturated linear orders and certain class of countably saturated graphs

Popis výsledku v původním jazyce

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality c. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality c, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From our proof it follows that this minimal linear order is a Fraïssé limit of certain Fraïssé class. In particular, it is homogeneous with respect to countable subsets. Next we prove the existence and uniqueness of the uncountable version of the random graph. This graph is isomorphic to (H(ω1) , ∈ ∪ ∋) , where H(ω1) is the set of hereditarily countable sets, and two sets are connected if one of them is an element of the other. In the last section, an example of a prime countably saturated Boolean algebra is presented.

Název v anglickém jazyce

On countably saturated linear orders and certain class of countably saturated graphs

Popis výsledku anglicky

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality c. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality c, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From our proof it follows that this minimal linear order is a Fraïssé limit of certain Fraïssé class. In particular, it is homogeneous with respect to countable subsets. Next we prove the existence and uniqueness of the uncountable version of the random graph. This graph is isomorphic to (H(ω1) , ∈ ∪ ∋) , where H(ω1) is the set of hereditarily countable sets, and two sets are connected if one of them is an element of the other. In the last section, an example of a prime countably saturated Boolean algebra is presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF16-34860L" target="_blank" >GF16-34860L: Logika a topologie v Banachových prostorech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Mathematical Logic

ISSN

0933-5846

e-ISSN

1432-0665

Svazek periodika

60

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

189-209

Kód UT WoS článku

000545545900001

EID výsledku v databázi Scopus

2-s2.0-85087498461