We show that Martin's Maximum${}^{++}$ implies Woodin's $\mathbb{P}_{\mathrm{max}}$ axiom $(*)$. This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply there are $?_2$ many real numbers.

Hardy property of means has been extensively studied by P\'ales and Pasteczka since 2016. The core this research is based on few their properties: concavity, symmetry, monotonicity, repetition invariance homogeneity (last axiom was recently omitted using some homogenizations techniques). In the present paper we deliver a study possible omitting monotonicity replacing weaker axiom. These results...

Abstract In this paper I will analyze and criticize Linsbichler’s recent proposition to interpret the fundamental axiom of Praxeology as analytic. first describe problem situation. then proposed solution his problem; namely interpretation argue that idea does not fully utilize critical potentials are available improve axiom. propose an alternative which call ‘critical interpretation’ conserves ...

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

We prove that the axiom system of basic algebras as given in Chajda and Emanovský (Discuss Math Gen Algebra Appl 24:31–42, 2004) is not independent. The axiom (BA3) can be deleted and the remaining axioms are shown to be independent. The case when the axiom of double negation is deleted is also treated.

We present a set of axioms that justify the use of belief functions to quantify the beliefs held by an agent Y at time t and based on Y's evidential corpus. It is essentially postulated that degrees of belief are quantified by a function in [0,1] that give the same degrees of beliefs to subsets that represent the same propositions according to Y's evidential corpus. We derive the impact of the ...