Timeline for Relation in mathematical logic vs Relation in Sets
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2021 at 9:11 | comment | added | Conifold | It is not quite true that predicate symbols in a language do not mean "anything". The formal language comes with axioms (of ordered fields, etc.), which "implicitly" define their "meaning", as Hilbert put it. That would be the intensional meaning as opposed to the extensional meaning given by sets in a structure. One can even make this "intension" precise as in modal logic by taking the models of the language (structures) to be the possible worlds. The intension is then the mentioned interpretation function that maps ("associates") predicate letters to relations in the structures. | |
| Feb 3, 2015 at 22:13 | comment | added | steakexchange | her ne kadar yorumlarda tesekkur etmek kurallara aykiri da olsa tesekkur ederim, aydinlandim. | |
| Feb 3, 2015 at 22:04 | vote | accept | steakexchange | ||
| Feb 3, 2015 at 21:50 | comment | added | Burak | The point of this answer is that there is no difference because "relations in context of FOL" simply does not mean anything without the actual set theoretic definition of relation. Whenever you are given a relation symbol, like $<$, whether or not the formula $< (x,y)$ is true is determined by whether or not the 2-tuple $(x,y)$ belongs to the interpretation of the relation symbol $<$, which is a subset of 2-fold cartesian product of your domain. | |
| Feb 3, 2015 at 21:46 | history | edited | Burak | CC BY-SA 3.0 | added 82 characters in body |
| Feb 3, 2015 at 21:45 | comment | added | steakexchange | thank you for the answer, it is a nice summary of key concepts, but my question actually is what is the difference between relations in context of sets and relations in context of FOL? are they the same concept or different? relations in sets don't seem to be same as relations in mathematical logic | |
| Feb 3, 2015 at 21:40 | history | answered | Burak | CC BY-SA 3.0 |