2
votes
2answers
601 views

All properties of a mathematical object

This is primarily a question about related literature. I am looking for specific references, or terminology that I can use to search for references. Let A a well defined mathematical structure of ...
2
votes
0answers
328 views

Relations of infinite arity

Infinitary logic considers languages being infinite by infinite conjunctions and disjunctions. I wonder why it not considers languages being infinite by relations and functions of infinite arity. ...
3
votes
0answers
272 views

To what extent MSO = WS1S, when adding relations?

Let me first clarify my definitions. For a word $w \in \Sigma^*$, with $\Sigma=\{a_1, \ldots, a_n\}$, I define two structures: $${\mathbb{N}}(w) = \langle {\mathbb{N}}, <, Q_{a_1}, \ldots, Q_{a_n} ...
0
votes
2answers
518 views

Theory interpreted in non-set domain of discourse may be consistent?

Following the blow. I will try to ask question in order to check if I well understand what was pointed. I decide to ask another question, because mathoverflow is not projected to be good environment ...
6
votes
3answers
494 views

What assumptions and methodology do metaproofs of logic theorems use and employ?

In logic modules, theorems like Soundness and completeness of first order logic are proved. Later, Godel's incompleteness theorem is proved. May I ask what are assumed at the metalevel to prove such ...