Reply to Ma ZF

Reply to comment by Ma and Zhang on ‘‘Rescaling the complementary relationship for land surface evaporation’’

Ma and Zhang (2017) note a concern they have with our rescaled Complementary Relationship (CR) for land surface evaporation when daily average wind speeds are very low (perhaps less than 1 m/s). We discuss conditions and specific formulations that lead to this concern, but ultimately argue that under these conditions, a key assumption behind the CR itself may not be satisfied at the daily time ...

Generalized Multisets: From ZF to FSM

We study generalized multisets (multisets that allow possible negative multiplicities) both in the Zermelo-Fraenkel framework and in the finitely supported mathematics. We extend the notion of generalized multiset over a finite alphabet, and we replace it by the notion of algebraically finitely supported generalized multiset over a possibly infinite alphabet. We analyze the correspondence betwe...

The Authors’ Reply

On the Use of Impredicative Reasoning to Construct a Class of Partial Models of ZF Within ZF PRELIMINARY UNPUBLISHED DRAFT

Gödel’s incompleteness results show that if ZF is consistent, it is impossible to construct within ZF itself a single object (set) that represents a complete and precise semantic model of ZF. Nevertheless, it has also become clear since then that many kinds of partial models can be constructed within ZF that reveal interesting characteristics of ZF and related formal systems. We develop here on...

On the Use of Impredicative Reasoning to Construct a Class of Partial Models of ZF Within ZF UNPUBLISHED DRAFT

Gödel’s incompleteness results show that if ZF is consistent, it is impossible to construct within ZF itself a single object (set) that represents a complete and precise semantic model of ZF. Nevertheless, it has also become clear since then that many kinds of partial models can be constructed within ZF that reveal interesting characteristics of ZF and related formal systems. We develop here on...