47 citations · 87 across the 29 of their papers we have counts for
5 papers · 1 filter
Nobody needs equations
Adonai Schlup Sant'Anna
Equations are ubiquitous in most mathematical activities. Nevertheless, in this paper it is shown how to do standard mathematics without any equation at all. More than that, it is…
Flow: the Axiom of Choice is independent from the Partition Principle in ZFU
Adonai Sant'Anna, Renato Brodzinski, Marcio de França +1
We introduce a formal theory called Flow where the intended interpretation of its terms is that of function. We prove ZF, ZFC and ZFU (ZF with atoms) can be immersed within Flow as…
Flow: the Axiom of Choice is independent from the Partition Principle
Adonai S. Sant'Anna, Otavio Bueno, Marcio P. P. de França +1
We introduce a general theory of functions called Flow. We prove ZF, non-well founded ZF and ZFC can be immersed within Flow as a natural consequence from our framework. The existe…
A critical study on the concept of identity in Zermelo-Fraenkel-like axioms
Aurelio Sartorelli, Decio Krause, Adonai S. Sant'Anna
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of i…
Indexed identity and fuzzy set theory
Adonai S. Sant'Anna
We introduce the concept of indexed identity, where the usual notion of identity is a particular case. Our mathematical framework allows us a generalized method for `indexing' pred…