A stronger form of the theorem constructing a rigid binary relation on any set
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 2001-07-02 | |
| dc.date | 2001-09-25 | |
| dc.date.accessioned | 2026-07-07T06:31:30Z | |
| dc.date.available | 2026-07-07T06:31:30Z | |
| dc.description | On every set A there is a rigid binary relation i.e. such a relation R \subseteq A \times A that there is no homomorphism (A,R) \rightarrow (A,R) except the identity (Vop{ě}nka et al. [1965]). We prove that for each infinite cardinal number κif card A \leq 2^κ, then there exists a relation R \subseteq A \times A with the following property: \forall (x \in A) \exists ({x} \subseteq A(x) \subseteq A, card A(x) \leq κ) \forall (f: A(x) \rightarrow A, f \neq id_A(x)) f is not a homomorphism of R. The above property implies that R is rigid. If a relation R \subseteq A \times A has the above property, then card A \leq 2^κ. | |
| dc.description | an enlarged version, 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0107009 | |
| dc.identifier | http://arxiv.org/abs/math/0107009 | |
| dc.identifier | Aequationes Mathematicae 66 (2003), pp. 257-260 | |
| dc.identifier | doi:10.1007/s00010-003-2676-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98624 | |
| dc.subject | Logic | |
| dc.subject | Combinatorics | |
| dc.subject | 03E05 (Primary), 08A35 (Primary) | |
| dc.title | A stronger form of the theorem constructing a rigid binary relation on any set | |
| dc.type | text |