Paraconsistent First-Order Logic with infinite hierarchy levels of contradiction $LP^#_{omega}$. Axiomatical system $HST^#_{omega}$, as paraconsistent generalization of Hrbacek set theory HST

In this paper paraconsistent first-order logic LP^{#}_{omega} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{omega} is discussed.Axiomatical system HST^{#}_{omega} as paraconsistent generalization of Hrbacek set theory HST is considered.