Ackermann functions are used recursively to define the transfinite cardinals of Cantor. Axiom of Monotonicity is defined and used to derive Continuum Hypothesis. Axiom of Fusion is defined and used to split the unit interval into infinitesimals

Sentient Arithmetic is defined as an extention of Elementary Arithmetic with three more derivation rules and the Incompleteness Theorems are derived within it without using any metalanguage. It is shown that Consistency cannot be chosen as an axiom

Directed paths are obtained by inverting a matrix with elements from a field, showing that it is unnecessary to go through the cumbersome procedure of inverting a matrix with elements from a division ring

It is shown that fractional voting system (FVS) can be used to circumvent Arrow's paradox. In the FVS, the input to the voting system is the preference distribution of the voters and not the usual preference order. As a consequence, it turns out that it is possible to associate a unique...

A set theory called Intuitive Set Theory is introduced in which Skolem Paradox does not appear. A measure function called real measure is defined in which Axiom of Choice cannot produce a nonmeasurable set

Two axioms which define intuitive set theory, Axiom of Combinatorial Sets and Axiom of Infinitesimals, are stated. Generalized Continuum Hypothesis is derived from the first axiom, and the infinitesimal is visualized using the latter

Intuitive set theory is defined as the theory we get when we add the axioms, Monotonicity and Fusion, to ZF theory. Axiom of Monotonicity makes the Continuum Hypothesis true, and the Axiom of Fusion splits the unit interval into infinitesimals