Here's a reference: Wolfgang Rautenberg, A Concise Introduction to Mathematical Logic, 3rd edition, Springer, 2010. On page 42 he defines the operations $+$ and $\cdot$ on $\mathbb N$ as having their "ordinary meaning". On page 62 he says that "interpretation" = "model". Finally, on pages 105-106 he defines $\mathcal N = (\mathbb N, 0, S, +, \cdot)$ and calls $\mathcal N$ the "standard model".

Here's a reference: Wolfgang Rautenberg, A Concise Introduction to Mathematical Logic, 3rd edition, Springer, 2010. On page 42 he defines the operations $+$ and $\cdot$ on $\mathbb N$ as having their "ordinary meaning". On page 62 he says that "interpretation" = "model". Finally, on pages 105-106 he defines $\mathcal N = (\mathbb N, 0, S, +, \cdot)$ and calls $\mathcal N$ the "standard model". ($\mathbb N$ is defined as the set of natural numbers including zero on page xix.)

Here's a reference: Wolfgang Rautenberg, A Concise Introduction to Mathematical Logic, 3rd edition, Springer, 2010. On page 62 he says that "interpretation" = "model". On page 105 he defines $\mathcal N = (\mathbb N, 0, S, +, \cdot)$, and on page 106 he calls $\mathcal N$ the "standard model".

Here's a reference: Wolfgang Rautenberg, A Concise Introduction to Mathematical Logic, 3rd edition, Springer, 2010. On page 42 he defines the operations $+$ and $\cdot$ on $\mathbb N$ as having their "ordinary meaning". On page 62 he says that "interpretation" = "model". Finally, on pages 105-106 he defines $\mathcal N = (\mathbb N, 0, S, +, \cdot)$ and calls $\mathcal N$ the "standard model".