# Article

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Keywords:
alternative set theory; cuts of natural numbers; inner and outer cut of a class; inner and outer product of two cuts; logarithmical cut
Summary:
Three complete characteristics of couples of nonadditive cuts such that $\underline{J\times K}\neq\overline{Jtimes K}$ are given. The equality $\overline{J\times K}=J\,!\,K$ is proved for all couples of nonadditive cuts. Some examples of nonadditive cuts are described.
References:
[KZ 1988] Kalina M., Zlatoš P.: Arithmetics of cuts and cuts of classes. Comment. Math. Univ. Carolinae 29 (1988), 435-456. MR 0972828
[KZ 1989] Kalina M., Zlatoš P.: Cuts of real classes. Comment. Math. Univ. Carolinae 30 (1989), 129-136. MR 0995711
[S 1988] Sochor A.: Addition of initial segments I. Comment. Math. Univ. Carolinae 29 (1988), 501-517. MR 0972833 | Zbl 0658.03030
[SV 1979] Sochor A., Vopěnka P.: Endomorphic universes and their standard extensions. Comment. Math. Univ. Carolinae 20 (1979), 605-629. MR 0555178
[SV 1980] Sochor A., Vopěnka P.: Revealments. Comment. Math. Univ. Carolinae 21 (1980), 97-118. MR 0566243
[Tz 1987] Tzouvaras A.: A notion of measure for classes in AST. Comment. Math. Univ. Carolinae 28 (1987), 449-455. MR 0912575 | Zbl 0629.03033
[Tz 1988] Tzouvaras A.: Correction to the paper Tz 1987. Comment. Math. Univ. Carolinae 29 (1988), 393. MR 0957408

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